Kenneth R. Szulczyk
At time t, we buy a T-day forward contract to exchange the domestic currency for foreign
currency at F. Thus, we exchange the domestic currency for the foreign currency, using the
contract, F. Then we obtain the following units of foreign currency, calculated in Equation 34.
360
T
1 +i
FS
d^ (34)^This strategy is not profitable if at time T, the amount we receive in foreign currency is less
or equal to than we pay for the foreign currency. Thus, arbitrage ensures we set the source of
funds from the foreign country equal to the use of the funds for the domestic country, yielding
Equation 35.
360
T
= 1 +i
360T
1 +i
FS
d f^ (35)^We solve for F to obtain Equation 36, which is the same as Equation 29. Consequently, two
different scenarios yield the same equation.
360
T
1 +i360
T
1 +i
F=S
fd
(36)Arbitrage adjustment process can be slow, and rates of returns can differ between countries.
Thus, international investors can exploit these differences to earn a higher rate of return. For
example, a U.S. investor can invest in the United States to earn 2% interest or invest in Japan to
earn 5%. He plans to invest for one year. Spot exchange rate is $0.0127 per yen while a one-year
forward contract equals $0.0120 per yen. Although the domestic country is the United States for
this investor, we reversed the exchange rate to conform to this analysis.
Investor calculates the rate of return to invest in the United States in Equation 37. Expected
rate of return equals 2%, which is identical to the U.S. interest rate.
1 0. 02
360
1 0. (^02)
360
1 +
360
T
rd 1 +id (37)Investor calculates the rate of return for his Japanese investment in Equation 38. An
investor would earn a negative return of 0.8. Although Japan has a greater interest rate, the
depreciating yen wipes out any gains from the higher interest rate. Hence, the investor should
invest in the United State where his or her return is greater.